Affiliation:
1. Inria Sophia-Antipolis, 2004 Route des Lucioles, 06902 Valbonne, France
2. Université Côte d’Azur/CNRS, 250 Rue Albert Einstein, 06560 Valbonne, France
Abstract
Abstract
The clustering coefficient has been introduced to capture the social phenomena that a friend of a friend tends to be my friend. This metric has been widely studied and has shown to be of great interest to describe the characteristics of a social graph. But, the clustering coefficient is originally defined for a graph in which the links are undirected, such as friendship links (Facebook) or professional links (LinkedIn). For a graph in which links are directed from a source of information to a consumer of information, it is no more adequate. We show that former studies have missed much of the information contained in the directed part of such graphs. In this article, we introduce a new metric to measure the clustering of directed social graphs with interest links, namely the interest clustering coefficient. We compute it (exactly and using sampling methods) on a very large social graph, a Twitter snapshot with 505 million users and 23 billion links, as well as other various datasets. We additionally provide the values of the formerly introduced directed and undirected metrics, a first on such a large snapshot. We observe a higher value of the interest clustering coefficient than classic directed clustering coefficients, showing the importance of this metric. By studying the bidirectional edges of the Twitter graph, we also show that the interest clustering coefficient is more adequate to capture the interest part of the graph while classic ones are more adequate to capture the social part. We also introduce a new model able to build random networks with a high value of interest clustering coefficient. We finally discuss the interest of this new metric for link recommendation.
Funder
French government through the UCA JEDI
Publisher
Oxford University Press (OUP)
Subject
Applied Mathematics,Computational Mathematics,Control and Optimization,Management Science and Operations Research,Computer Networks and Communications
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